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Adapting to unknown disturbance autocorrelation in regression with long memory

By Javier Hidalgo and Peter Robinson


We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency–domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non–normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss–Markov efficient with standard convergence rate. Despite the anomalous behavior of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency–domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included

Topics: HB Economic Theory
Publisher: Wiley-Blackwell on behalf of the Econometric Society
Year: 2002
DOI identifier: 10.1111/1468-0262.00341
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Provided by: LSE Research Online
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